Aubrey tiene un nuevo estuche de arte con forma de prisma rectangular. El estuche es de 12 cm por 20 cm por 5cm. Lo único dentro del estuche es un nuevo borrador rosa con las dimensiones que se muestran a continuación.

¿Cual es el volumen del estuche que no ocupa por el borrador?

Answer:

[tex]\|a\| = 5\sqrt{13}[/tex].

[tex]\|b\| = 3\sqrt{29}[/tex].

Step-by-step explanation:

Let [tex]m[/tex],[tex]n[/tex], and [tex]k[/tex] be scalars such that:

[tex]\displaystyle a = m\, (2\, \vec{i} + 3\, \vec{j}) = m\, \begin{bmatrix}2 \\ 3\end{bmatrix}[/tex].

[tex]\displaystyle b = n\, (2\, \vec{i} + 5\, \vec{j}) = n\, \begin{bmatrix}2 \\ 5\end{bmatrix}[/tex].

[tex]\displaystyle (a + b) = k\, (8\, \vec{i} + 15\, \vec{j}) = k\, \begin{bmatrix}8 \\ 15\end{bmatrix}[/tex].

The question states that [tex]\| a + b \| = 34[/tex]. In other words:

[tex]k\, \sqrt{8^{2} + 15^{2}} = 34[/tex].

[tex]k^{2} \, (8^{2} + 15^{2}) = 34^{2}[/tex].

[tex]289\, k^{2} = 34^{2}[/tex].

Make use of the fact that [tex]289 = 17^{2}[/tex] whereas [tex]34 = 2 \times 17[/tex].

[tex]\begin{aligned}17^{2}\, k^{2} &= 34^{2}\\ &= (2 \times 17)^{2} \\ &= 2^{2} \times 17^{2} \end{aligned}[/tex].

[tex]k^{2} = 2^{2}[/tex].

The question also states that the scalar multiple here is positive. Hence, [tex]k = 2[/tex].

Therefore:

[tex]\begin{aligned} (a + b) &= k\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 2\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 16\, \vec{i} + 30\, \vec{j}\\ &= \begin{bmatrix}16 \\ 30 \end{bmatrix}\end{aligned}[/tex].

[tex](a + b)[/tex] could also be expressed in terms of [tex]m[/tex] and [tex]n[/tex]:

[tex]\begin{aligned} a + b &= m\, (2\, \vec{i} + 3\, \vec{j}) + n\, (2\, \vec{i} + 5\, \vec{j}) \\ &= (2\, m + 2\, n) \, \vec{i} + (3\, m + 5\, n) \, \vec{j} \end{aligned}[/tex].

[tex]\begin{aligned} a + b &= m\, \begin{bmatrix}2\\ 3 \end{bmatrix} + n\, \begin{bmatrix} 2\\ 5 \end{bmatrix} \\ &= \begin{bmatrix}2\, m + 2\, n \\ 3\, m + 5\, n\end{bmatrix}\end{aligned}[/tex].

Equate the two expressions and solve for [tex]m[/tex] and [tex]n[/tex]:

[tex]\begin{cases}2\, m + 2\, n = 16 \\ 3\, m + 5\, n = 30\end{cases}[/tex].

[tex]\begin{cases}m = 5 \\ n = 3\end{cases}[/tex].

Hence:

[tex]\begin{aligned} \| a \| &= \| m\, (2\, \vec{i} + 3\, \vec{j})\| \\ &= m\, \| (2\, \vec{i} + 3\, \vec{j}) \| \\ &= 5\, \sqrt{2^{2} + 3^{2}} = 5 \sqrt{13}\end{aligned}[/tex].

[tex]\begin{aligned} \| b \| &= \| n\, (2\, \vec{i} + 5\, \vec{j})\| \\ &= n\, \| (2\, \vec{i} + 5\, \vec{j}) \| \\ &= 3\, \sqrt{2^{2} + 5^{2}} = 3 \sqrt{29}\end{aligned}[/tex].

Answer:

The common for the second question is 30

Answer:

39/30 Here 30 will be common in denominators

Step-by-step explanation:

6/15×2/2=12/30

3/10×3/3=9/30

3/5×6/6=18/30

= 12/30+9/30+18/30

39/30

Answer:

0.0347 = constant of proportionality

[tex]1 * e^{0.0347t} = 15000[/tex]

Step-by-step explanation:

Given

[tex]1*e^{0.0347t}[/tex]

Solving (a): what does 0.0347 represent?

An exponential model is represented as:

[tex]f(t) = a * e^{kt}[/tex]

Where:

[tex]k \to[/tex] constant of proportionality

So, by comparison:

[tex]k = 0.0347[/tex]

Hence:

[tex]0.0347 \to[/tex] constant of proportionality

Solving (b): Formula to calculate when balance equals 15000

To do this, we simply equate the formula to 15000.

So, we have:

[tex]1 * e^{0.0347t} = 15000[/tex]

Answer:

1.) (2,1) is a solution

2.) (4,3) is NOT a solution

Step-by-step explanation:

1.) (2,1)

These are these mean (x,y)

2=x and 1=y

You want to substitute the numbers for the letters in the equation.

so.

2(2)+1=5

4+1=5

5=5, This statement is true so (2,1) is a solution.

2.) Same as above. 4=x and 3=y

4(4)-3(3)=10

16-9=10

7 Does Not Equal 10, Therefore, (4,3) is Not a solution to the equation.

Answer:

(2x + y) ( x + 2y)

Step-by-step explanation:

Answer:

2x - 19

Step-by-step explanation:

Perimeter = sum of sides

First let's simplify each side

We can simplify each side by using distributive property. Distributive property is where you multiply the number on the outside of the parenthesis by the numbers on the inside of the parenthesis.

2(x + 5)

Distribute by multiplying x and 5 by 2

2 * x = 2x and 2 * 5 = 10

2x + 10

1/2(4x + 8)

Distribute by multiplying 4x and 8 by 1/2

1/2 * 4x = 2x and 1/2 * 8 = 4

2x + 4

-3(2x + 11)

Distribute by multiplying 2x and 11 by -3

-3 * 2x = -6x

-3 * -33

-6x - 33

Finally add all the simplified expressions ( remember that they represent the side lengths of the triangle )

2x + 10 + 2x + 4 - 6x - 33

Combine like terms

2x + 2x - 6x = -2x

10 + 4 - 33 = -19

Perimeter: -2x - 19

Answer:

Perimeter = - 2x - 19

Step-by-step explanation:

[tex]Perimeter \: of \: a \: triangle \\ = Sum \: of \: the \: length \: of \: all \: sides \\ = [2(x+5)]+[-3(2x+11)]+[ \frac{1}{2} (4x+8)] \\ = [(2 \times x)+(2 \times 5)]+[(-3 \times 2x)+( - 3 \times 11)]+[ (\frac{1}{2} \times 4x) + ( \frac{1}{2} \times 8)] \\ = (2x + 10) + ( - 6x - 33) + (2x + 4) \\ = 2x + 10 - 6x - 33 + 2x + 4 \\ = 2x - 6x + 2x + 10 - 33 + 4 \\ = - 2x - 19[/tex]

So, the perimeter is - 2x - 19.

Answer:

Divide 278 by 4 and the remainder value is the amount of leftover brownies.

278 ÷ 4 = 69, remainder of 2

Therefore, he had 2 brownies left.

Answer:

No

Step-by-step explanation:

It can still be 8x - 2

first of all you collect like terms

5x + 3x - 2

= 8x -2

Answer: 4,000

Step-by-step explanation: To round 4,327 to the nearest thousand, we first find the digit in the rounding place, which in this case is the 4 in the thousands place. Next, we look at the digit to the right of the 4, which is 3.

According to the rules of rounding, since the digit to

the right of the rounding place is less than 5, we round down.

So the 4 in the rounding place stays the same

and all digits to the right of the 4 become 0.

So 4,327 rounded to the nearest thousand is 4,000.

Answer:

[tex] {2}^{1 \div 2[/tex]

Answer:

If 4 flower pots cost 4.08 dollars, then 1 flower pot costs 4.08/4 dollars.

4.08/4 = 1.02.

So the unit price is $1.02.

Let me know if this helps!

Answer:

x is 7

EF is 10

FG is 12

Step-by-step explanation:

[tex]EF + FG = EG \\ (4x - 18) + (3x - 9) = 22 \\ 7x - 27 = 22 \\ 7x = 49 \\ x = 7[/tex]

then substitute:

[tex]EF = 4x - 18 \\ EF = 4(7) - 18 \\EF = 28 - 18 \\ EF = 10[/tex]

[tex]FG = 3x - 9 \\ FG = 3(7) - 9 \\FG = 21 - 9 \\ FG = 12[/tex]

First question:

BC + BA = CA

BC = CA - BA

BC = 36 - 9

BC = 27

Answer:

there is always a y-intercept in all graphs.

Step-by-step explanation:

be it a line graph, quadratic graph or cubic graph. all graphs will definitely have a y-intercept. and in this case, since y=mx + c where c is the y-intercept. the y intercept of this graph is 10

Find the circumference of the pond:

Circumference = 2 x pi x radius

Circumference = 2 x 3.14 x 7.7 = 48.356 m

You want to go around 3 times so multiply the circumference by 3:

48.356 x 3 = 145.068m

Rounded to 1 decimal = 145.1m

Answer:

Yes, it is a polynomial, and the degree is 5

Step-by-step explanation:

A polynomial is a combination of terms separated using + or − signs and normally have exponents. So, this equation is a polynomial. The degree is just the highest exponential value, which is 5 because -5y is being raised to the 5th power

Step-by-step explanation:

Y=

[tex]y = 10 - 8x \\ put \: this \: in \: the \: second \: equation \\ 2(10 - 8x) - 4x = 40 \\ 20 - 16x - 4x = 40 \\ 20 - 20x = 40 \\ - 20 = 20x \\ x = - 1 \\ put \: the \: value \: of \: x \: in \: th \: first \: equation \\ y = 10 - 8( - 1) \\ y = 10 + 8 \\ y = 18[/tex]

Hence, x=-1 and y=18

Answer:

(- 1, 18 )

Step-by-step explanation:

Given the equations

y + 8x = 10 ( subtract 8x from both sides )

y = 10 - 8x → (1)

2y - 4x = 40 → (2)

Substitute y = 10 - 8x into (2)

2(10 - 8x) - 4x = 40 ← distribute and simplify left side

20 - 16x - 4x = 40

20 - 20x = 40 ( subtract 20 from both sides )

- 20x = 20 ( divide both sides by - 20 )

x = - 1

Substitute x = - 1 into (1) for corresponding value of y

y = 10 - 8(- 1) = 10 + 8 = 18

solution is (- 1, 18 )

Assuming you want to do a cartesian product, then you basically form items (x,y)  such that x is in set A, and y is in set A

More generally, A * B will consist of items of the form (x,y) such that x is in A and y is in B. However, we have B = A.

So,

A * A = {

(a,a), (a,b), (a,c)

(b,a), (b,b), (b,c)

(c,a), (c,b), (c,c)

}

I broke things up into separate rows to show that we can form a 3x3 table. Each row is a different x value from the set {a,b,c}. Each column is a different y value from the set {a,b,c}

In my opinion, this helps organize things much better than rather have it all on one single line like this

A * A = { (a,a), (a,b), (a,c), (b,a), (b,b), (b,c), (c,a), (c,b), (c,c) }

which in all honesty looks like a bit of a cluttered mess.

Answer:

Step-by-step explanation:

A={a,b,c}

A×A={a×a,a×b,a×c,b×a,b×b,b×c,c×a,c×b,c×c}

here's the answer to your question

Answer:

False

Step-by-step explanation:

It only cuts the risk as stated and other factors such as lifestyle, age, bloodpressure and past medical background also have an impact so you can still have heart issues.

Answer:

20 miles

Step-by-step explanation:

She ran 20miles, at the same point she passed her friend

Answer:

h=6

Step-by-step explanation:

9514 1404 393

Answer:

  x = 90°

Step-by-step explanation:

Half the sum of x and 120° is the angle where the chords cross, 105°. Then ...

  105° = (1/2)(x +120°)

  210° = x + 120°

  210° -120° = x = 90°

_____

Additional comment

z is the arc that finishes the circle: 360° -90° -68° -120° = 82°.

Answer:

1

Step-by-step explanation:

1

Step-by-step explanation:

Using R, I used the following code to create a histogram:

bowling.scores <- c(87, 104, 79, 94, 117, 82, 72, 116, 105, 95, 88, 93, 109, 119, 75,  

                   103, 112, 97, 73, 85, 91, 86, 102, 99, 106, 84, 98, 83, 81, 96, 92)

data.frame(bowling.scores)

ggplot(data.frame(bowling.scores), aes(x=bowling.scores)) +  

 xlim(c(70, 120)) +

 scale_y_continuous(breaks = seq(0, 10, by=1), "Frequency") +

 geom_histogram(breaks=seq(70, 120, by=10), color="black", fill="grey60") +

 labs(title="Histogram of Bowling Scores", x="Bowling Scores", y="Frequency")

Answer:

5555+2929

= 8484

its an irrational no.

thanks

Answer:

square of 31 is 961

Step-by-step explanation:

31^2

31×31

=961